Question

10. The sum of two numbers is 20, and their difference is 2whole 1by 2.
Find the ratio of the numbers.​

Answer 1

Answer

Let the Numbers be x and y.

Given that ;

• x + y = 20
• x - y = 2 whole 1/2 = 5/2

★ x + y = 20 --(i)

=> x = 20 - y

Putting the Value of x in (ii)

★ x - y = 5/2 --(ii)

=> 20 - y - y = 5/2

=> 20 - 2y = 5/2

=> 20 - 5/2 = 2y

=> (40 - 5)/2 = 2y

=> 35/2 = 2y

=> y = 35/4

Putting Value of y in (i)

=> x = 20 - y

=> x = 20 - 35/4

=> x = (80 - 35)/4

=> x = 45/4

_____________________________

➡ Ratio of x and y

➡ x : y

➡ 45/4 : 35/4

➡ 9 : 7

Answer 2

AnswEr :

⠀

$\huge\red {\boxed{ \bold{x : y = 9 : 7}}}$

⠀

Explanation :

▣ Given :

• Sum of two Numbers is 20

• Difference of that Number is $\large\tt{2\frac{1}{2}}$

▣ To Find :

• Ratio of the Numbers.

▣ Solution :

Let the Numbers be x and, y.

• x + y = 20
• x - y = $\large\tt{</strong><strong>2</strong><strong>\frac{1}{2}}$ = $\large\tt{\frac{</strong><strong>5</strong><strong>}{2}}$

A.T.Q.

➟ x + y = 20

➟ x - y = $\large\tt{\frac{5}{2}}$

________________

➟ x + x = 20 + $\large\tt{\frac{5}{2}}$

➟ 2x = $\large\tt{\frac{(40+5)}{2}}$

➟ 2x = $\large\tt{\frac{45}{2}}$

➟ x = $\huge\tt{\frac{45}{4}}$

━━━━━━━━━━━━━━━━━━━━━━━━

✯ Using the Value of x as $\</u><u>l</u><u>a</u><u>r</u><u>ge\tt{\frac{45}{4}}$

➟ x + y = 20

➟ y = 20 - x

➟ y = 20 - $\large\tt{\frac{45}{4}}$

➟ y = $\large\tt{\frac{(80-45)}{4}}$

➟ y = $\huge\tt{\frac{35}{4}}$

━━━━━━━━━━━━━━━━━━━━━━━━

▣ Ratio of x and y is -

$\Rightarrow \bold{x : y}$

$\large\Rightarrow \bold{ \frac{45}{4} : \frac{35}{4} }$

$\scriptsize \blacksquare \: \bold{dividing \: each \: term \: by \: \frac{5}{4} }$

$\huge\Rightarrow \bold{9 : 7}$